Figure 1.
Framework of Cluster-based Oversampling with Boosting
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2020, 3(1): 1-9.
doi: 10.3934/mfc.2020001
A novel approach for solving skewed classification problem using cluster based ensemble method
| 1. | Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh, India – 522502 |
| 2. | Vellore Institute of Technology, Chennai Campus, Chennai, 600127, Tamilnadu, India |
In numerous real-world applications, the class imbalance problem is prevalent. When training samples of one class immensely outnumber samples of the other classes, the traditional machine learning algorithms show bias towards the majority class (a class with more number of samples) lead to significant losses of model performance. Several techniques have been proposed to handle the problem of class imbalance, including data sampling and boosting. In this paper, we present a cluster-based oversampling with boosting algorithm (Cluster+Boost) for learning from imbalanced data. We evaluate the performance of the proposed approach with state-of-the-art methods based on ensemble learning like AdaBoost, RUSBoost and SMOTEBoost. We conducted experiments on 22 data sets with various imbalance ratios. The experimental results are promising and provide an alternative approach for improving the performance of the classifier when learned on highly imbalanced data sets.
Mathematics Subject Classification:
Primary: 58F15, 58F17; Secondary: 53C35.
Citation:
Gillala Rekha, V Krishna Reddy, Amit Kumar Tyagi. A novel approach for solving skewed classification problem using cluster based ensemble method. Mathematical Foundations of Computing,
2020, 3
(1)
: 1-9.
doi: 10.3934/mfc.2020001
![]()
References:
| [1] |
A. Ali, S. M. Shamsuddin and A. L. Ralescu,
Classification with class imbalance problem: A review, Int J Adv Soft Comput Appl, 7 (2015), 176-204.
|
| [2] |
J. Alcalá-Fdez, L. Sánchez, S. Garcia, M. J. del Jesus, S. Ventura, J. M. Garrell, J. Otero, C. Romero, J. Bacardit and V. M. Rivas,
Keel: A software tool to assess evolutionary algorithms for data mining problems, Soft Computing, 13 (2009), 307-318.
|
| [3] |
C. Bunkhumpornpat, K. Sinapiromsaran and C. Lursinsap, Safe-level-smote: Safe-level-synthetic minority over-sampling technique for handling the class imbalanced problem, in: Proceedings of the IEEE Pacific-Asia Conference on Knowledge Discovery and Data Mining, Springer, 5476 (2009), 475–482.
doi: 10.1007/978-3-642-01307-2_43. |
| [4] |
S. Barua, M. M. Islam, X. Yao and K. Murase,
Mwmote–majority weighted minority oversampling technique for imbalanced data set learning, IEEE Transactions on Knowledge and Data Engineering, 26 (2014), 405-425.
doi: 10.1109/TKDE.2012.232. |
| [5] |
A. P. Bradley,
The use of the area under the roc curve in the evaluation of machine learning algorithms, Pattern Recognition, 30 (1997), 1145-1159.
doi: 10.1016/S0031-3203(96)00142-2. |
| [6] |
N. V. Chawla, K. W. Bowyer, L. O. Hall and W. P. Kegelmeyer,
Smote: Synthetic minority over-sampling technique, Journal of Artificial Intelligence Research, 16 (2002), 321-357.
doi: 10.1613/jair.953. |
| [7] |
N. V. Chawla, A. Lazarevic, L. O. Hall and K. W. Bowyer, Smoteboost: Improving prediction of the minority class in boosting, in: European Conference on Principles of Data Mining and Knowledge Discovery, Springer, 2003,107–119.
doi: 10.1007/978-3-540-39804-2_12. |
| [8] |
M. Galar, A. Fernandez, E. Barrenechea, H. Bustince and F. Herrera,
A review on ensembles for the class imbalance problem: Bagging-, boosting-, and hybrid-based approaches,, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 42 (2012), 463-484.
doi: 10.1109/TSMCC.2011.2161285. |
| [9] |
V. García, R. A. Mollineda and J. S. Sánchez,
On the k-nn performance in a challenging scenario of imbalance and overlapping,, Pattern Analysis and Applications, 11 (2008), 269-280.
doi: 10.1007/s10044-007-0087-5. |
| [10] |
H. He, Y. Bai, E. A. Garcia and S. Li, Adasyn: Adaptive synthetic sampling approach for imbalanced learning, in: Proceedings of the IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), IEEE, 2008, 1322–1328. |
| [11] |
S. Hu, Y. Liang, L. Ma and Y. He, Msmote: Improving classification performance when training data is imbalanced, in: Proceedings of the Second International Workshop on Computer Science and Engineering, IEEE, 2 (2009), 13–17.
doi: 10.1109/WCSE.2009.756. |
| [12] |
H. Han, W.-Y. Wang and B.-H. Mao, Borderline-smote: A new over-sampling method in imbalanced data sets learning, in: Proceedings of the International Conference on Intelligent Computing, Springer, 2005,878–887.
doi: 10.1007/11538059_91. |
| [13] |
M. Krstic and M. Bjelica,
Impact of class imbalance on personalized program guide performance, IEEE Transactions on Consumer Electronics, 61 (2015), 90-95.
doi: 10.1109/TCE.2015.7064115. |
| [14] |
M. Lin, K. Tang and X. Yao,
Dynamic sampling approach to training neural networks for multiclass imbalance classification, IEEE Transactions on Neural Networks and Learning Systems, 24 (2013), 647-660.
|
| [15] |
W.-Z. Lu and D. Wang,
Ground-level ozone prediction by support vector machine approach with a cost-sensitive classification scheme, Science of the Total Environment, 395 (2008), 109-116.
doi: 10.1016/j.scitotenv.2008.01.035. |
| [16] |
W.-C. Lin, C.-F. Tsai, Y.-H. Hu and J.-S. Jhang,
Clustering-based undersampling in class-imbalanced data, Information Sciences, 409/410 (2017), 17-26.
doi: 10.1016/j.ins.2017.05.008. |
| [17] |
G. Rekha, A. K. Tyagi and V. Krishna Reddy,
A wide scale classification of class imbalance problem and its solutions: A systematic literature review,, Journal of Computer Science, 15 (2019), 886-929.
doi: 10.3844/jcssp.2019.886.929. |
| [18] |
G. Rekha, A. K. Tyagi and V. Krishna Reddy,
Solving class imbalance problem using bagging, boosting techniques, with and without using noise filtering method, International Journal of Hybrid Intelligent Systems, 15 (2019), 67-76.
doi: 10.3233/HIS-190261. |
| [19] |
F. Rayhan, S. Ahmed, A. Mahbub, M. Jani, S. Shatabda and D. M. Farid, et al., Cusboost: Cluster-based under-sampling with boosting for imbalanced classification, 2017 2nd International Conference on Computational Systems and Information Technology for Sustainable Solution (CSITSS), (2017), arXiv1712.04356.
doi: 10.1109/CSITSS.2017.8447534. |
| [20] |
S. Ruggieri,
Efficient c4. 5 [classification algorithm], IEEE Transactions on Knowledge and Data Engineering, 14 (2002), 438-444.
|
| [21] |
Y. Sun, A. K. Wong and M. S. Kamel,
Classification of imbalanced data: A review,, International Journal of Pattern Recognition and Artificial Intelligence, 23 (2009), 687-719.
doi: 10.1142/S0218001409007326. |
| [22] |
C. Seiffert, T. M. Khoshgoftaar, J. Van Hulse and A. Napolitano,
Rusboost: A hybrid approach to alleviating class imbalance, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 40 (2010), 185-197.
doi: 10.1109/TSMCA.2009.2029559. |
| [23] |
R. C. Team, R: A language and environment for statistical computing [internet], vienna (austria): R foundation for statistical computing.[cited 2015 mar 23] (2012). |
| [24] |
S. Wang and X. Yao, Diversity analysis on imbalanced data sets by using ensemble models, in: Proceedings of the IEEE Symposium on Computational Intelligence and Data Mining, IEEE, 2009,324–331.
doi: 10.1109/CIDM.2009.4938667. |
show all references
References:
| [1] |
A. Ali, S. M. Shamsuddin and A. L. Ralescu,
Classification with class imbalance problem: A review, Int J Adv Soft Comput Appl, 7 (2015), 176-204.
|
| [2] |
J. Alcalá-Fdez, L. Sánchez, S. Garcia, M. J. del Jesus, S. Ventura, J. M. Garrell, J. Otero, C. Romero, J. Bacardit and V. M. Rivas,
Keel: A software tool to assess evolutionary algorithms for data mining problems, Soft Computing, 13 (2009), 307-318.
|
| [3] |
C. Bunkhumpornpat, K. Sinapiromsaran and C. Lursinsap, Safe-level-smote: Safe-level-synthetic minority over-sampling technique for handling the class imbalanced problem, in: Proceedings of the IEEE Pacific-Asia Conference on Knowledge Discovery and Data Mining, Springer, 5476 (2009), 475–482.
doi: 10.1007/978-3-642-01307-2_43. |
| [4] |
S. Barua, M. M. Islam, X. Yao and K. Murase,
Mwmote–majority weighted minority oversampling technique for imbalanced data set learning, IEEE Transactions on Knowledge and Data Engineering, 26 (2014), 405-425.
doi: 10.1109/TKDE.2012.232. |
| [5] |
A. P. Bradley,
The use of the area under the roc curve in the evaluation of machine learning algorithms, Pattern Recognition, 30 (1997), 1145-1159.
doi: 10.1016/S0031-3203(96)00142-2. |
| [6] |
N. V. Chawla, K. W. Bowyer, L. O. Hall and W. P. Kegelmeyer,
Smote: Synthetic minority over-sampling technique, Journal of Artificial Intelligence Research, 16 (2002), 321-357.
doi: 10.1613/jair.953. |
| [7] |
N. V. Chawla, A. Lazarevic, L. O. Hall and K. W. Bowyer, Smoteboost: Improving prediction of the minority class in boosting, in: European Conference on Principles of Data Mining and Knowledge Discovery, Springer, 2003,107–119.
doi: 10.1007/978-3-540-39804-2_12. |
| [8] |
M. Galar, A. Fernandez, E. Barrenechea, H. Bustince and F. Herrera,
A review on ensembles for the class imbalance problem: Bagging-, boosting-, and hybrid-based approaches,, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 42 (2012), 463-484.
doi: 10.1109/TSMCC.2011.2161285. |
| [9] |
V. García, R. A. Mollineda and J. S. Sánchez,
On the k-nn performance in a challenging scenario of imbalance and overlapping,, Pattern Analysis and Applications, 11 (2008), 269-280.
doi: 10.1007/s10044-007-0087-5. |
| [10] |
H. He, Y. Bai, E. A. Garcia and S. Li, Adasyn: Adaptive synthetic sampling approach for imbalanced learning, in: Proceedings of the IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), IEEE, 2008, 1322–1328. |
| [11] |
S. Hu, Y. Liang, L. Ma and Y. He, Msmote: Improving classification performance when training data is imbalanced, in: Proceedings of the Second International Workshop on Computer Science and Engineering, IEEE, 2 (2009), 13–17.
doi: 10.1109/WCSE.2009.756. |
| [12] |
H. Han, W.-Y. Wang and B.-H. Mao, Borderline-smote: A new over-sampling method in imbalanced data sets learning, in: Proceedings of the International Conference on Intelligent Computing, Springer, 2005,878–887.
doi: 10.1007/11538059_91. |
| [13] |
M. Krstic and M. Bjelica,
Impact of class imbalance on personalized program guide performance, IEEE Transactions on Consumer Electronics, 61 (2015), 90-95.
doi: 10.1109/TCE.2015.7064115. |
| [14] |
M. Lin, K. Tang and X. Yao,
Dynamic sampling approach to training neural networks for multiclass imbalance classification, IEEE Transactions on Neural Networks and Learning Systems, 24 (2013), 647-660.
|
| [15] |
W.-Z. Lu and D. Wang,
Ground-level ozone prediction by support vector machine approach with a cost-sensitive classification scheme, Science of the Total Environment, 395 (2008), 109-116.
doi: 10.1016/j.scitotenv.2008.01.035. |
| [16] |
W.-C. Lin, C.-F. Tsai, Y.-H. Hu and J.-S. Jhang,
Clustering-based undersampling in class-imbalanced data, Information Sciences, 409/410 (2017), 17-26.
doi: 10.1016/j.ins.2017.05.008. |
| [17] |
G. Rekha, A. K. Tyagi and V. Krishna Reddy,
A wide scale classification of class imbalance problem and its solutions: A systematic literature review,, Journal of Computer Science, 15 (2019), 886-929.
doi: 10.3844/jcssp.2019.886.929. |
| [18] |
G. Rekha, A. K. Tyagi and V. Krishna Reddy,
Solving class imbalance problem using bagging, boosting techniques, with and without using noise filtering method, International Journal of Hybrid Intelligent Systems, 15 (2019), 67-76.
doi: 10.3233/HIS-190261. |
| [19] |
F. Rayhan, S. Ahmed, A. Mahbub, M. Jani, S. Shatabda and D. M. Farid, et al., Cusboost: Cluster-based under-sampling with boosting for imbalanced classification, 2017 2nd International Conference on Computational Systems and Information Technology for Sustainable Solution (CSITSS), (2017), arXiv1712.04356.
doi: 10.1109/CSITSS.2017.8447534. |
| [20] |
S. Ruggieri,
Efficient c4. 5 [classification algorithm], IEEE Transactions on Knowledge and Data Engineering, 14 (2002), 438-444.
|
| [21] |
Y. Sun, A. K. Wong and M. S. Kamel,
Classification of imbalanced data: A review,, International Journal of Pattern Recognition and Artificial Intelligence, 23 (2009), 687-719.
doi: 10.1142/S0218001409007326. |
| [22] |
C. Seiffert, T. M. Khoshgoftaar, J. Van Hulse and A. Napolitano,
Rusboost: A hybrid approach to alleviating class imbalance, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 40 (2010), 185-197.
doi: 10.1109/TSMCA.2009.2029559. |
| [23] |
R. C. Team, R: A language and environment for statistical computing [internet], vienna (austria): R foundation for statistical computing.[cited 2015 mar 23] (2012). |
| [24] |
S. Wang and X. Yao, Diversity analysis on imbalanced data sets by using ensemble models, in: Proceedings of the IEEE Symposium on Computational Intelligence and Data Mining, IEEE, 2009,324–331.
doi: 10.1109/CIDM.2009.4938667. |
Table 1.
Dataset Characteristics
| Datasets | Size | # attr | % IR |
| ecoli-0_vs_1 | 220 | 7 | 1.82 |
| ecoli1 | 336 | 7 | 3.36 |
| ecoli2 | 336 | 7 | 5.46 |
| ecoli3 | 336 | 7 | 8.6 |
| glass0 | 214 | 9 | 2.06 |
| glass-0-1-2-3_vs_4-5-6 | 214 | 9 | 3.2 |
| glass1 | 214 | 9 | 1.82 |
| glass6 | 214 | 9 | 6.38 |
| haberman | 306 | 3 | 2.78 |
| iris0 | 150 | 4 | 2 |
| new-thyroid1 | 215 | 5 | 5.14 |
| new-thyroid2 | 215 | 5 | 5.14 |
| page-blocks0 | 5472 | 10 | 8.79 |
| pima | 768 | 8 | 1.87 |
| segment0 | 2308 | 19 | 6.02 |
| vehicle0 | 846 | 18 | 3.25 |
| vehicle1 | 846 | 18 | 2.9 |
| vehicle2 | 846 | 18 | 2.88 |
| vehicle3 | 846 | 18 | 2.99 |
| wisconsin | 683 | 9 | 1.86 |
| yeast1 | 1484 | 8 | 2.46 |
| yeast3 | 1484 | 8 | 8.1 |
| Datasets | Size | # attr | % IR |
| ecoli-0_vs_1 | 220 | 7 | 1.82 |
| ecoli1 | 336 | 7 | 3.36 |
| ecoli2 | 336 | 7 | 5.46 |
| ecoli3 | 336 | 7 | 8.6 |
| glass0 | 214 | 9 | 2.06 |
| glass-0-1-2-3_vs_4-5-6 | 214 | 9 | 3.2 |
| glass1 | 214 | 9 | 1.82 |
| glass6 | 214 | 9 | 6.38 |
| haberman | 306 | 3 | 2.78 |
| iris0 | 150 | 4 | 2 |
| new-thyroid1 | 215 | 5 | 5.14 |
| new-thyroid2 | 215 | 5 | 5.14 |
| page-blocks0 | 5472 | 10 | 8.79 |
| pima | 768 | 8 | 1.87 |
| segment0 | 2308 | 19 | 6.02 |
| vehicle0 | 846 | 18 | 3.25 |
| vehicle1 | 846 | 18 | 2.9 |
| vehicle2 | 846 | 18 | 2.88 |
| vehicle3 | 846 | 18 | 2.99 |
| wisconsin | 683 | 9 | 1.86 |
| yeast1 | 1484 | 8 | 2.46 |
| yeast3 | 1484 | 8 | 8.1 |
Table 2.
Performances of the sampling techniques across all datasets using AUC Metric
| Datasets | AdaBoost | RUSBoost | SMOTEBoost | Cluster+boost |
| ecoli-0_vs_1 | 0.6354 | 0.794 | 0.799 | 0.992 |
| ecoli1 | 0.778 | 0.883 | 0.899 | 0.985 |
| ecoli2 | 0.703 | 0.899 | 0.967 | 0.97 |
| ecoli3 | 0.681 | 0.856 | 0.955 | 0.986 |
| glass0 | 0.74 | 0.813 | 0.912 | 0.974 |
| glass-0-1-2-3_vs_4-5-6 | 0.703 | 0.91 | 0.987 | 0.987 |
| glass1 | 0.952 | 0.763 | 0.985 | 0.987 |
| glass6 | 0.947 | 0.918 | 0.991 | 0.997 |
| haberman | 0.947 | 0.656 | 0.947 | 0.942 |
| iris0 | 0.949 | 0.98 | 0.978 | 0.981 |
| new-thyroid1 | 0.947 | 0.975 | 0.947 | 0.986 |
| new-thyroid2 | 0.687 | 0.961 | 0.987 | 0.994 |
| page-blocks0 | 0.637 | 0.953 | 0.967 | 0.996 |
| pima | 0.6223 | 0.751 | 0.897 | 0.899 |
| segment0 | 0.996 | 0.994 | 0.998 | 0.998 |
| vehicle0 | 0.943 | 0.965 | 0.968 | 0.978 |
| vehicle1 | 0.754 | 0.768 | 0.897 | 0.899 |
| vehicle2 | 0.854 | 0.966 | 0.967 | 0.978 |
| vehicle3 | 0.745 | 0.763 | 0.894 | 0.894 |
| wisconsin | 0.9 | 0.96 | 0.994 | 0.894 |
| yeast1 | 0.7589 | 0.7382 | 0.741 | 0.996 |
| yeast3 | 0.93 | 0.944 | 0.944 | 0.994 |
| Datasets | AdaBoost | RUSBoost | SMOTEBoost | Cluster+boost |
| ecoli-0_vs_1 | 0.6354 | 0.794 | 0.799 | 0.992 |
| ecoli1 | 0.778 | 0.883 | 0.899 | 0.985 |
| ecoli2 | 0.703 | 0.899 | 0.967 | 0.97 |
| ecoli3 | 0.681 | 0.856 | 0.955 | 0.986 |
| glass0 | 0.74 | 0.813 | 0.912 | 0.974 |
| glass-0-1-2-3_vs_4-5-6 | 0.703 | 0.91 | 0.987 | 0.987 |
| glass1 | 0.952 | 0.763 | 0.985 | 0.987 |
| glass6 | 0.947 | 0.918 | 0.991 | 0.997 |
| haberman | 0.947 | 0.656 | 0.947 | 0.942 |
| iris0 | 0.949 | 0.98 | 0.978 | 0.981 |
| new-thyroid1 | 0.947 | 0.975 | 0.947 | 0.986 |
| new-thyroid2 | 0.687 | 0.961 | 0.987 | 0.994 |
| page-blocks0 | 0.637 | 0.953 | 0.967 | 0.996 |
| pima | 0.6223 | 0.751 | 0.897 | 0.899 |
| segment0 | 0.996 | 0.994 | 0.998 | 0.998 |
| vehicle0 | 0.943 | 0.965 | 0.968 | 0.978 |
| vehicle1 | 0.754 | 0.768 | 0.897 | 0.899 |
| vehicle2 | 0.854 | 0.966 | 0.967 | 0.978 |
| vehicle3 | 0.745 | 0.763 | 0.894 | 0.894 |
| wisconsin | 0.9 | 0.96 | 0.994 | 0.894 |
| yeast1 | 0.7589 | 0.7382 | 0.741 | 0.996 |
| yeast3 | 0.93 | 0.944 | 0.944 | 0.994 |
Table 3.
Performances of the sampling techniques across all datasets using F-measure Metric
| Datasets | AdaBoost | RUSBoost | SMOTEBoost | Cluster+Boost |
| ecoli-0_vs_1 | 0.632 | 0.795 | 0.799 | 0.995 |
| ecoli1 | 0.778 | 0.89 | 0.899 | 0.992 |
| ecoli2 | 0.71 | 0.899 | 0.967 | 0.986 |
| ecoli3 | 0.681 | 0.856 | 0.955 | 0.964 |
| glass0 | 0.74 | 0.813 | 0.912 | 0.982 |
| glass-0-1-2-3_vs_4-5-6 | 0.703 | 0.91 | 0.987 | 0.995 |
| glass1 | 0.952 | 0.763 | 0.985 | 0.99 |
| glass6 | 0.947 | 0.918 | 0.991 | 0.994 |
| haberman | 0.947 | 0.656 | 0.947 | 0.942 |
| iris0 | 0.949 | 0.98 | 0.894 | 0.993 |
| new-thyroid1 | 0.947 | 0.975 | 0.947 | 0.983 |
| new-thyroid2 | 0.687 | 0.961 | 0.987 | 0.983 |
| page-blocks0 | 0.637 | 0.953 | 0.967 | 0.998 |
| pima | 0.6223 | 0.751 | 0.897 | 0.894 |
| segment0 | 0.996 | 0.994 | 0.998 | 0.998 |
| vehicle0 | 0.943 | 0.965 | 0.988 | 0.984 |
| vehicle1 | 0.754 | 0.768 | 0.897 | 0.894 |
| vehicle2 | 0.854 | 0.966 | 0.967 | 0.941 |
| vehicle3 | 0.745 | 0.763 | 0.894 | 0.894 |
| wisconsin | 0.9 | 0.96 | 0.994 | 0.997 |
| yeast1 | 0.7589 | 0.7382 | 0.741 | 0.979 |
| yeast3 | 0.93 | 0.944 | 0.944 | 0.974 |
| Datasets | AdaBoost | RUSBoost | SMOTEBoost | Cluster+Boost |
| ecoli-0_vs_1 | 0.632 | 0.795 | 0.799 | 0.995 |
| ecoli1 | 0.778 | 0.89 | 0.899 | 0.992 |
| ecoli2 | 0.71 | 0.899 | 0.967 | 0.986 |
| ecoli3 | 0.681 | 0.856 | 0.955 | 0.964 |
| glass0 | 0.74 | 0.813 | 0.912 | 0.982 |
| glass-0-1-2-3_vs_4-5-6 | 0.703 | 0.91 | 0.987 | 0.995 |
| glass1 | 0.952 | 0.763 | 0.985 | 0.99 |
| glass6 | 0.947 | 0.918 | 0.991 | 0.994 |
| haberman | 0.947 | 0.656 | 0.947 | 0.942 |
| iris0 | 0.949 | 0.98 | 0.894 | 0.993 |
| new-thyroid1 | 0.947 | 0.975 | 0.947 | 0.983 |
| new-thyroid2 | 0.687 | 0.961 | 0.987 | 0.983 |
| page-blocks0 | 0.637 | 0.953 | 0.967 | 0.998 |
| pima | 0.6223 | 0.751 | 0.897 | 0.894 |
| segment0 | 0.996 | 0.994 | 0.998 | 0.998 |
| vehicle0 | 0.943 | 0.965 | 0.988 | 0.984 |
| vehicle1 | 0.754 | 0.768 | 0.897 | 0.894 |
| vehicle2 | 0.854 | 0.966 | 0.967 | 0.941 |
| vehicle3 | 0.745 | 0.763 | 0.894 | 0.894 |
| wisconsin | 0.9 | 0.96 | 0.994 | 0.997 |
| yeast1 | 0.7589 | 0.7382 | 0.741 | 0.979 |
| yeast3 | 0.93 | 0.944 | 0.944 | 0.974 |
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